Metasurface waveguide couplers

ABSTRACT

This disclosure provides various examples and methods of manufacturing metasurface couplers, including slanted grating metasurface couplers characterized by a plurality of parallel, elongated angled ridges. In some examples, a transmission-mode metasurface coupler with a slanted grating is used to couple optical radiation into a waveguide. In some examples, a reflection-mode metasurface coupler with a slanted grating and reflective layer is used to couple optical radiation into a waveguide.

PRIORITY APPLICATIONS

This application is a divisional application of U.S. patent applicationSer. No. 18/170,549 filed on Feb. 17, 2023 with the same title, whichapplication claims benefit under 35 U.S.C. § 119(e) and priority to U.S.Provisional Patent Application No. 63/365,116, filed on May 20, 2022,titled “Through-Waveguide Reflective Metasurface Couplers,” whichapplication is hereby incorporated by reference in its entirety.

TECHNICAL FIELD

This disclosure relates to metamaterial optical devices to control thedeflection of optical radiation. This disclosure also relates to opticalwaveguides, including optical waveguides for conveying red, green, andblue (RGB) optical radiation for image display, image projection, andimage capture.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-1C illustrate examples of optical paths through concave,convex, and flat plate optical lenses, respectively, according tovarious embodiments.

FIG. 2A illustrates a top-down view of an example representation of apattern of deflector elements for a metasurface structure, according toone embodiment.

FIG. 2B illustrates an enlarged perspective view of the examplerepresentation of the pattern of deflector elements in the metasurfaceof FIG. 2A, according to one embodiment.

FIG. 3A illustrates an example block diagram of a side view of ametasurface with nanopillar deflectors positioned on a substrate,according to one embodiment.

FIG. 3B illustrates the example block diagram of the metasurface of FIG.3A operating to reflect incident optical radiation, according to oneembodiment.

FIG. 3C illustrates the example block diagram of the metasurface of FIG.3A steering incident optical radiation, according to one embodiment.

FIGS. 4A-4B illustrate metasurfaces used in conjunction withlaser-scanning subsystems, according to various embodiments.

FIG. 5A illustrates an example system with a metasurface and waveguideused in conjunction with a laser scanning subsystem, according to oneembodiment.

FIG. 5B illustrates an example display system that utilizes input andoutput metasurfaces in conjunction with a waveguide, according to oneembodiment.

FIG. 6A illustrates an example of a cell of a metasurface for redoptical radiation, according to one embodiment.

FIG. 6B illustrates an example of a cell of a metasurface for greenoptical radiation, according to one embodiment.

FIG. 6C illustrates an example of a cell of a metasurface for blueoptical radiation, according to one embodiment.

FIG. 7A illustrates an example of a two-dimensional RGB cell of ametasurface, according to one embodiment.

FIG. 7B illustrates a perspective view of a two-dimensional RGB cell ofa metasurface, according to one embodiment.

FIG. 8 illustrates an example of a multi-pixel array of RGB cells ofmetasurfaces, according to one embodiment.

FIG. 9A illustrates a multi-pixel array of RGB cells of metasurfacesused to couple optical radiation into a waveguide, according to oneembodiment.

FIG. 9B illustrates a side view of a system with a display to generateoptical radiation and a metasurface to couple the optical radiation intoa waveguide, according to one embodiment.

FIG. 9C illustrates a top view of the system of FIG. 9B, according toone embodiment.

FIG. 10A illustrates an example of a metasurface with rectangular ridgesto couple optical radiation into a waveguide, according to oneembodiment.

FIG. 10B illustrates a metasurface with rectangular ridges couplingoptical radiation from a display engine into a waveguide, according toone embodiment.

FIGS. 11A-C illustrate simulated graphs of diffraction efficiencies ofmetasurfaces of rectangular ridges for red, green, and blue opticalradiation, according to various embodiments.

FIG. 12 illustrates an example of a metasurface coupler comprising aslanted grating of angled ridges to couple optical radiation into awaveguide, according to one embodiment.

FIGS. 13A-D illustrate an example diagram of a manufacturing process fora metasurface coupler, according to one embodiment.

FIG. 13E illustrates a reflective layer deposited on the angled ridgesof the slanted grating metasurface, according to one embodiment.

FIG. 13F illustrates an alternative embodiment with a reflective coatingon angled ridges of the slanted grating metasurface, according to oneembodiment.

FIG. 14 illustrates a perspective view of a portion of a metasurfacecoupler, according to one embodiment.

FIG. 15 illustrates an optical system with a metasurface coupler tocouple optical radiation into a waveguide, according to one embodiment.

FIGS. 16A-C illustrate simulated graphs of the waveguide couplingefficiencies of slanted grating metasurface for red, green, and blueoptical radiation, according to various embodiments.

FIG. 17 illustrates a slanted grating metasurface with elongated angledridges of amorphous silicon formed directly on a high-index glasswaveguide, according to one embodiment.

FIG. 18 illustrates an example of an optical system with a slantedgrating metasurface coupler with elongated angled ridges of siliconnitride directly on a glass or sapphire waveguide, according to variousembodiments.

FIGS. 19A-J illustrate a diagram of a manufacturing process for ametasurface coupler, according to one embodiment.

FIGS. 20A-C illustrate a diagram of an additive ion beam etching processto form the elongated slanted ridges of silicon nitride of a slantedgrating, according to one embodiment.

FIG. 21 illustrates an example image of elongated angled ridges ofsilicon nitride on a glass substrate, according to one embodiment.

FIG. 22 illustrates an example graph of the height of elongated angledridges of silicon nitride along the length of a glass substrate,according to one embodiment.

FIG. 23 illustrates a perspective view of an optical device with aslanted grating metasurface coupler with a plurality of elongatedsilicon nitride angled ridges directly on a glass waveguide, accordingto one embodiment.

FIG. 24A illustrates a diagram of an optical system with a slantedgrating metasurface coupler of elongated silicon nitride angled ridgesto couple optical radiation into a waveguide, according to oneembodiment.

FIG. 24B illustrates a close-up image of a portion of the slantedgrating metasurface coupler, according to one embodiment.

DETAILED DESCRIPTION

Various systems and apparatuses are described herein, along with methodsof manufacturing such systems and apparatuses, that operate to deflectoptical radiation into a waveguide for conveyance along a lengththereof. Various examples of optical metasurfaces are described hereinfor operation in the visible spectrum. Metasurfaces may be used, forexample, to couple optical radiation into waveguides of near-eyedisplays (NEDs), such as head-mounted displays (HMD) and wearabledisplays. An input coupler or “in-coupler” may be formed as ametasurface to couple an image source to a waveguide. The waveguide mayconvey the optical radiation along the length thereof for subsequentprocessing, free-space transmission, projection, and/or output via anoutput coupler. In some embodiments, the output coupler may comprise ametasurface or grating, as described herein, to decouple opticalradiation from the waveguide instead.

For example, an output coupling metasurface may deflect and focus theoptical radiation (e.g., based on the frequency thereof and/or with afrequency selective filter) to form an image visible to one eye of auser. In some embodiments, the output coupling metasurface may be usedto deflect and focus the optical radiation as a stereo image or as aduplicated image on both eyes of the user or even on the eyes ofmultiple users.

Various embodiments described herein are configured to operate inconjunction with an electronic display. In one example, a multi-pixelLED display generates optical radiation at various wavelengths (e.g.,different visible colors of light) using at least three different colorsof LED subpixels (e.g., red, green, and blue subpixels for an RGBdisplay). A metasurface layer may include a plurality of metasurfacesubpixels. Each metasurface subpixel may correspond to one of the LEDsubpixels. In some embodiments, a multi-frequency metasurface subpixelmay be responsive to multiple frequencies allowing a singlemulti-frequency metasurface subpixel to be used for each pixel of theRGB display.

In some embodiments described herein, a transmission metasurfacecomprises a metasurface of rectangular ridges of polysilicon (Poly-Si).The rectangular ridges may be formed with interelement spacings,heights, and widths selected to couple a broad spectrum of opticalradiation, or at least specific wavelengths of optical radiation (e.g.,red, green, and blue wavelengths), into an optical waveguide.

The embodiments described above operate to couple optical radiation froman optical radiation source through the metasurface into an opticalwaveguide. More specifically, the metasurface receives the opticalradiation in the first instance and deflects it into the opticalwaveguide at an angle for total internal reflection (TIR) within thewaveguide. As such, the optical radiation enters the optical waveguidefor the first time at an angle greater than or equal to a critical anglefor total internal reflection and conveyance along the length of theoptical waveguide. As used herein, the term critical angle or θ_(c)refers to the smallest angle of incidence that yields total reflectionwithin the waveguide, such that total internal reflection occurs whenthe angle of incidence is greater than the critical angle.

In contrast to the transmission approach above, other embodimentsdescribed herein include a metasurface that operates to reflect opticalradiation into the waveguide for total internal reflection. In some suchembodiments, a metasurface is utilized in a configuration in which theoptical radiation travels from an optical radiation source through thewaveguide before being deflected by the metasurface back into thewaveguide. The optical radiation travels through the waveguide at anangle greater than the critical angle, such that the optical radiationpasses through the optical waveguide. After passing through thewaveguide, the optical radiation is reflected by the metasurface backinto the waveguide at an angle less than the critical angle for totalinternal reflection within and conveyance along the length of thewaveguide.

According to various embodiments, a metasurface is configured to coupleoptical radiation into a waveguide and is formed as a slanted grating ofelongated angled ridges, such as elongated angled ridges whosecross-section approximates a triangle (e.g., a right triangle). Aslanted grating metasurface may be formed on a planar surface of awaveguide. The slanted grating metasurface includes an array ofelongated angled ridges that extend parallel to one another along thewidth of the waveguide surface. The elongated angled ridges may beshaped to approximate right-angle triangular polyhedrons that extendalong the width of the waveguide and deflect optical radiation forconveyance along the length of the waveguide. The elongated angledridges of the slanted grating may be formed directly on the surface ofthe waveguide. Alternatively, the elongated angled ridges of the slantedgrating may be formed in a base layer of material that is depositeddirectly on the surface of the waveguide, where a thin base layerremains between the slanted grating of elongated angled ridges and thewaveguide surface.

As an example, the slanted grating metasurface may be formed as aone-dimensional array of angled ridges of silicon nitride (SiNx)directly on a glass or sapphire waveguide. In some embodiments, theangled ridges of silicon nitride may extend from a thin residual baselayer of silicon nitride on the glass or sapphire waveguide. In variousembodiments, a reflective metallic layer is deposited on the angledridges of the slanted grating to reflect optical radiation with highefficiency. The heights, interelement spacing (pitch or distance betweenadjacent angled ridges), and the relative angles of the faces of each ofthe angled ridges are selected to deflect optical radiation back intothe underlying waveguide at an angle less than or equal to the criticalangle for total internal reflection within the waveguide.

For example, the slanted grating may include a plurality of elongatedangled ridges, where the cross-section of each elongated angled ridgeapproximates a right triangle. The hypotenuse face of each elongatedangled ridge (e.g., of silicon nitride) in the slanted grating may forman angle between 15 and 25 degrees relative to the planar face of thewaveguide. Each elongated angled ridge may extend to a height betweenapproximately 70 nanometers and 200 nanometers and the spacing or pitchbetween adjacent elongated silicon nitride angled ridges may be between300 and 500 nanometers. Accordingly, the dimensions of the elements inthe slanted grating metasurface are referred to as “subwavelength” sincethey are smaller than the wavelengths of light being deflected.

According to various embodiments, an optical system comprises awaveguide, an optical source to generate optical radiation, and ametasurface to couple the optical radiation into the waveguide. Theoptical source may generate optical radiation that is incident on afirst face of the waveguide at an angle of incidence at which theoptical radiation passes through the waveguide and out of a second,opposing face of the waveguide.

The metasurface may be positioned on a second face of the waveguide toreceive the optical radiation that passes through the waveguide from theoptical source. The metasurface operates to reflect the opticalradiation back into the waveguide at an angle greater than the criticalangle for total internal reflection within the waveguide. The opticalradiation may then be conveyed along the length of the waveguide.

Any of a wide variety of optical radiation sources may be used inconjunction with metasurface couplers including, without limitation, anarray of lasers, an array of light-emitting diodes (LEDs), an array ofmicro-LEDs, and/or an array of organic light-emitting diodes (OLEDs).

As described herein according to various embodiments, the metasurfacemay be embodied as or include a slanted grating of angled ridges thatextend along a width of the waveguide (i.e., perpendicular to the lengthof the waveguide). One or more reflective metallic layers may beoverlaid on the upper surface (the surface opposite the surface incontact with the waveguide) of the elongated angled ridges. The slantedgrating may be, for example, formed as an array of elongated angledridges in a silicon nitride layer deposited on the second face of thewaveguide.

As an example, each elongated angled ridge in the slanted grating mayhave a cross-section that approximates a triangle, such that each of theelongated angled ridges has a shape approximating a triangularpolyhedron. In some examples, each elongated angled ridge in the slantedgrating may have a cross-section that approximates a right triangle,such that each of the elongated angled ridges has a shape approximatinga right-angle triangular polyhedron.

In such embodiments, each elongated angled ridge in the slanted gratingmay include a base face that is co-planar with the waveguide, a heightface that extends from the base face to a target height (e.g., 70-200nanometers) at a steep angle approaching 90 degrees relative to the baseface, and an angled face (or hypotenuse face) that extends between theedge of the base face and an edge of the height face at a targetinternal angle to deflect the optical radiation for total internalreflection within the waveguide. An example of a suitable targetinternal angle for the angled or hypotenuse face of an elongated angledridge is 20 degrees for deflection of red, green, and blue opticalradiation. In other embodiments with elongated angled ridges havingdifferent dimensions and/or for operation at different wavelengths, theangle of the angled face or hypotenuse face relative to the base face ofeach elongated angled ridge in the slanted grating may vary betweenapproximately 15 and 25 degrees.

Many of the elements described herein are characterized or described interms of triangles, squares, rectangles, and other geometric shapes andcorresponding polyhedrons for convenience only. It is appreciated bythose of skill in the art that microfabrication and nanofabricationtechniques, such as lithography techniques, deposition techniques,etching techniques, ion beam etching, and the like are imprecise in someinstances. As such, an element described as being embodied as orapproximating a specific geometric shape or volume with one or more“corners,” “edges,” or “faces” may include fabrication imperfections,such as rounded corners, imperfect planar faces, and/or rounded edges.As such, descriptions of elements throughout this disclosure that areprovided in the context of geometric shapes, geometric polyhedrons,planar faces or surfaces, edges, or corners should be understood in thecontext of the nanofabrication techniques applicable to the scale of theelement being described or characterized.

As an example, at least some corners or edges of elongated angled ridgesforming a slanted grating of a slanted grating metasurface may berounded. As another example, an elongated angled ridge described ashaving a right-angle triangular cross-section with a height faceextending perpendicular to a base face is understood to encompass aheight face that is not perfectly planar and/or that extendsquasi-perpendicular from the base face, based on the limitations offabrication at the nanometer scale. For example, depending on thespecific limitations of manufacturing and fabrication processesutilized, an elongated angled ridge having a triangular cross-sectionmay have a height face that is modeled as or approximates beingperpendicular to a base face (e.g., 90 degrees) even though the actualangle may measure between 70 and 110 degrees and/or exhibit somenonuniformity between different elements in the same array.

The presently described metasurfaces, including variously describedmetasurface couplers, can be fabricated or otherwise manufactured usingany of a wide variety of nanofabrication techniques, various materials,various deposition and etching processes, nanofeature lithographytechniques, and the like. One example of a method to manufacture ametasurface coupler on a glass or sapphire waveguide substrate includesan initial deposition of a silicon nitride layer directly on a planarface of the waveguide substrate. In such an embodiment, the opticalradiation is anticipated to be received through an opposing planar faceof the waveguide substrate. A conductive layer, such as a metal layer ordoped semiconductor layer, is then deposited on the silicon nitride tofacilitate electron beam lithography.

The conductive layer is coated with a photoresist, such as a negativetone deep-ultraviolet (DUV) photoresist like ma-N series photoresists.The photoresist is processed (patterned, developed, and/or etched orotherwise removed) to define a plurality of elongated rectangularpolyhedrons of photoresist (e.g., elongated rectangular cuboids ofphotoresist) that extend perpendicular to a length dimension of thewaveguide substrate. For example, electron beam lithography may be usedto pattern a photoresist. The undeveloped negative photoresist (ordeveloped photoresist in the case of positive photoresists) is removedto reveal elongated rectangular cuboids of developed photoresist thateach have a width between 70 and 130 nanometers and are spaced from oneanother by a spacing gap between 300 and 400 nanometers.

The portions of the conductive layer between the elongated rectangularcuboids are exposed once the undeveloped photoresist is removed. Theexposed portions of the conductive layer are etched or otherwise removed(e.g., via reactive-ion etching). The exposed silicon nitride layerbetween the elongated rectangular cuboids of photoresist is etched to atarget depth. The remaining photoresist (e.g., the elongated rectangularcuboids of photoresist) is removed to expose the silicon nitride layerin its entirety.

The exposed silicon nitride layer includes a thin base layer of siliconnitride (e.g., 30-70 nanometers) with a plurality of elongatedrectangular ridges of silicon nitride extending therefrom (e.g.,extending an additional 70-130 nanometers above the base layer,depending on a target final height to be attained). The spacing betweenthe elongated rectangular ridges of silicon nitride defines theperiodicity (e.g., related to the frequency response) of the structures.The elongated rectangular ridges of silicon nitride act as “backstops”for the ion beam milling/etching process, as described below. Thesilicon nitride layer is milled at an angle using ion beam milling foradditive formation of a slanted grating as a one-dimensional array ofparallel elongated angled ridges of silicon nitride extending from aslightly thinner remaining base layer of silicon nitride on thewaveguide substrate. The elongated rectangular ridges of silicon nitrideact as backstops during the ion beam milling process to capture removedsilicon nitride from the base layer, resulting in the formation ofelongated angled ridges of silicon nitride.

A metallic layer is deposited on the upper exposed surfaces of theelongated angled ridges. In some embodiments, the metallic layer mayinclude a relatively thick optically reflective metal layer (e.g., atleast 100 nanometers thick). The optically reflective metal layer mayinclude various combinations of noble metals, such as silver (Ag), gold(Au), aluminum (Al), and/or any other materials that are highlyreflective at operational wavelengths. In some embodiments, the metalliclayer may further include a relatively thin adhesion metallic layer(e.g., between 1 and 5 nanometers thick) positioned between theoptically reflective metal layer and the elongated triangular ridges ofsilicon nitride to reduce delamination of the metallic layer from thesilicon nitride. Examples of suitable materials for such an adhesionlayer include, but are not limited to, titanium (Ti) and chromium (Cr).

Notably, the example process described above utilizes ion beam etchingor milling at an angle as part of an additive process. Ion beam etchingis traditionally used to remove material, as implied by the nameincluding “etching” or “milling.” The presently described method offabrication utilizes ion beam etching to remove some silicon nitridematerial from the base layer between two elongated rectangular ridges ofsilicon nitride for immediate relocation of at least some of the removedmaterial against the vertical face of one of the elongated rectangularcuboids. As illustrated in the figures and described in greater detailbelow, the removed and relocated silicon nitride material forms a slopedsurface against the elongated rectangular cuboid of silicon nitride,such that the elongated rectangular cuboids of silicon nitride becomeelongated angled ridges of silicon nitride having a cross-sectionapproaching a triangle, or more specifically in some embodiments, aright triangle, and are elongated along the width of a waveguide.

Whereas ion beam etching is typically considered a removal process,utilizing an ion beam etching process at an angle with respect to andwithin the nanometer-scale valleys defined between adjacentnanometer-scale ridges results in an unconventional additive process.Additionally, the angle at which the ion beam etches the silicon nitrideis inversely proportional to the target internal angle of the angledface or, in the case of an elongated angled ridge with a cross-sectionapproximating a right triangle, the hypotenuse face.

An understanding of traditional optical lenses may be helpful tounderstand the possible applications and functions of variousembodiments and applications of the metasurfaces described herein.Traditional optical lenses and mirrors (e.g., glass or acrylic) areformed with a curvature to modify the optical path of incident opticalradiation. Multiple lenses and/or mirrors may be combined with variousindices of refraction, curvatures, coatings, and other features toachieve specific optical deflection (refraction or reflection) goals.

FIGS. 1A-1C illustrate examples of optical paths through concave,convex, and flat plate optical lenses 110, 120, and 130, respectively.Specifically, FIG. 1A illustrates an example of a concave lens 110 thatreceives incident optical radiation 115 that is deflected as divergentoptical radiation 117. FIG. 1B illustrates incident optical radiation125 that converges as converging optical radiation 127 as it passesthrough the convex lens 120.

FIG. 1C illustrates incident optical radiation 135 incident at an anglerelative to a planar surface of a flat plate optical lens 130. An outputoptical radiation 137 is shifted as it passes through the flat plateoptical lens 130. The degree or amount of phase shift is based on adifference between the refractive index of surrounding media (e.g., air,water, waveguide, etc.) and the refractive index of the flat plateoptical lens 130. Convex, concave, and other shapes of mirrors can beused to achieve other manipulations of incident optical radiation.

Metamaterial-based lenses and mirrors may be formed as relatively thin(e.g., <1 mm) elements that provide controlled deflection without curvedsurfaces. As described herein, a substrate surface may be configured toallow optical radiation to pass through or to reflect optical radiationtherefrom. Subwavelength-scale features (e.g., pillars, gratings,etchings, slots, grooves, gaps, cavities, etc.) may be patterned on asurface of the substrate to deflect incident optical radiation in acontrolled manner to obtain a target optical radiation output at variousoutput angles (e.g., between 0° to 180°). In some embodiments,subwavelength-scale features may be formed on more than one surface ofthe substrate. For example, subwavelength-scale features may be formedon one or both sides of a substrate. A metasurface may be used todeflect (e.g., focus, collimate, diverge, scatter, etc.) opticalradiation within free space (e.g., air) or to couple optical radiationbetween free space and another medium, such as a waveguide, traditionaloptical lenses, a fiber optic transmission line, or the like.

In some embodiments, a metasurface may be used in place of injectionoptics for a laser-based scanning illumination engine or LEDmicrodisplay coupled to a waveguide. The metasurface may be used toefficiently deflect incident optical radiation from a laser source intoa waveguide for total internal reflection.

Variations of the systems and methods described herein may be used oradapted for use in near-to-eye (NTE) displays, such as NTE displays usedin wearable technology, smart glasses, augmented reality headsets,virtual reality headsets, heads-up displays, and the like. For example,a metasurface may be used as part of an NTE display to collimate opticalradiation into parallel rays for delivery to the eye of the user at“infinite focus.” Similarly, a metasurface may be used as part of an NTEdisplay to deliver optical radiation to the eye of the user at targetangles that vary spatially along the surface of the metasurface to causean image to appear to originate from one or more target focal depthplane(s). In some embodiments, the optical radiation may be covered atmultiple different depth planes to map the output optical radiation ontothe physical world and/or to relieve eye fatigue (i.e.vergence-accommodation conflict or VAC).

In other embodiments, a metasurface may be used as part of an NTEdisplay to duplicate source images and cause the duplicated sourceimages to appear as if they originate from different positions in thevisual field, for example, to facilitate pupil replication or expansionof an effective “eyebox” of the NTE display. The metasurface may be usedto expand the source image of an NTE display to have a wider range ofdivergence angles (e.g., act as an expander) to provide a widereffective field of view.

Variations of the systems and methods described herein may be used oradapted for use in light-field displays. As used herein, the term“light-field display” is used to describe any of a wide variety ofdisplays using various technologies to render a three-dimensional imagefield to one or more users without the use of polarized oractive-shutter glasses. Light-field displays deliver an image to eacheye of the user at slightly different perspectives to provide binoculardisparity for depth perception. The different images transmitted to theeyes of the user cause the user to perceive the image as athree-dimensional image. As an example, a lenticular lens overlaid on adigital display may be used to deliver different images to each eye ofthe user. Three-dimensional displays using lenticular lens technologyhave fundamentally limited fields of view.

The presently described systems and methods relating to metasurfaces aresuitable to create advanced light-field displays that can be viewed fromdifferent perspectives simultaneously by multiple users. Similarly,metasurfaces can be used to create advanced light-field displays thatdeliver an image from different perspectives as a single user movesthrough the visual field. The metasurfaces may deliver variations of animage to different spatial locations within the visual field to providethe user with a natural-appearing three-dimensional image that accountsfor motion, parallax, occlusion, and/or accommodation.

Some three-dimensional displays use a two-dimensional array ofmicrolenses (e.g., a microlens array or MLA) with lenslets that spanmultiple pixels of the underlying electronic display. In suchembodiments, the microlenses cause the user to perceive only one of theunderlying pixels based on the position of the user's eye relative toeach respective lenslet. The metasurface-based approaches describedherein avoid undesirable field-of-view, reduced fill factor, and otheroptical deficiencies fundamentally associated with microlens solutions.Specifically, three-dimensional displays utilizing metasurfaces todeliver different images (e.g., different perspectives of an image) todifferent locations within the visual field provide an improved opticalperformance, a finer pitch, near 100% fill factor, and a lower profilethan comparable microlens-based solutions.

According to various embodiments, the metasurfaces described herein maybe fabricated using any of a wide variety of suitable manufacturingtechniques, including without limitation nanoimprinting manufacturingtechniques, complementary metal-oxide-semiconductor (CMOS) fabricationtechniques, and/or deep or extreme ultraviolet (DUV or EUV) lithographyprocesses. For example, such processes may be used to fabricate thematerial layers herein that form an array of etchings, gaps, pillars,slots, channels, grooves, or other deflector elements.

In various embodiments, an array of polarization-independent, passivedeflector elements is patterned on a substrate through which opticalradiation passes (transmission mode) or from which optical radiation isreflected (reflection mode). The passive deflector elements may beadapted to deflect a relatively narrow band of coherent opticalradiation (e.g., from a laser light source) in a prescribed direction,arbitrarily based on the origin of the optical radiation (e.g.,pixel-by-pixel variation), and/or collimated to provide an effective“infinite focus.”

The generalized descriptions of the systems and methods herein may beutilized and/or adapted for utilization in a wide variety of industrial,commercial, and personal applications. Similarly, the presentlydescribed systems and methods may be used in conjunction with or utilizeexisting computing devices and infrastructures. Some of theinfrastructure that can be used with embodiments disclosed herein isalready available, such as general-purpose computers, computerprogramming tools and techniques, digital storage media, andcommunication links. A computing device or controller may include aprocessor, such as a microprocessor, a microcontroller, logic circuitry,or the like.

A processor may include one or more special-purpose processing devices,such as application-specific integrated circuits (ASICs), a programmablearray logic (PAL), a programmable logic array (PLA), a programmablelogic device (PLD), a field-programmable gate array (FPGA), or anothercustomizable and/or programmable device. The computing device may alsoinclude a machine-readable storage device, such as non-volatile memory,static RAM, dynamic RAM, flash memory, or another machine-readablestorage medium. Various aspects of certain embodiments may beimplemented using hardware, software, firmware, or a combinationthereof.

The components of the disclosed embodiments, as generally described andillustrated in the figures herein, could be arranged and designed in awide variety of different configurations. Furthermore, the features,structures, and operations associated with one embodiment may be appliedto or combined with the features, structures, or operations described inconjunction with another embodiment. In many instances, well-knownstructures, materials, or operations are not shown or described indetail to avoid obscuring aspects of this disclosure. The embodiments ofthe systems and methods provided within this disclosure are not intendedto limit the scope of the disclosure but are merely representative ofpossible embodiments. In addition, the steps of a method do notnecessarily need to be executed in any specific order or evensequentially, nor do the steps need to be executed only once, unless thecontext or express statements dictate otherwise.

FIG. 2A illustrates a top-down view of an example representation of apattern of deflector elements 210 for a metasurface structure, accordingto one embodiment. As illustrated, a uniform square grid of deflectorelements 210 may pattern the deflector elements 210 with uniformspacings between adjacent or nearest neighbor deflector elements.Moreover, the deflector elements 210 may be configured with uniformheights. In the illustrated example, the deflector elements 210 comprisecircular pillars arranged in a repeating pattern of pillar diameters.

FIG. 2B illustrates an enlarged perspective view of the examplerepresentation of the pattern of deflector elements in the metasurfaceof FIG. 2A, according to one embodiment. As illustrated, an array ofdeflector elements 220 includes a uniformly spaced arrangement ofcircular pillars (e.g., cylinders) extending from a substrate. Thedeflector elements 220 have different pillar diameters that increasealong one dimension (left to right) and are constant along the otherdimension (top to bottom). Alternative patterns of pillar diameters maybe used to achieve target deflection patterns.

FIG. 3A illustrates an example block diagram of a side view of ametasurface 300 with nanopillar deflector elements 330 positioned on asubstrate 350, according to one embodiment. As illustrated, thenanopillar deflector elements 330 may have a uniform height, H, andvarying diameters, D. In the illustrated example, the nanopillardeflector elements 330 are evenly spaced with a nearest neighboron-center spacing distance, P. The spacing between the centers ofadjacent or nearest neighbor nanopillars may be constant despite thevarying diameters of the pillars. As described herein, the dimensions,patterns, and spacings of the nanopillars are selected to achieve atarget deflection pattern (e.g., angle of deflection) and frequencyresponse (e.g., target operational bandwidth of optical radiation).

FIG. 3B illustrates the example block diagram of the metasurface 300 ofFIG. 3A operating to reflect incident optical radiation 370 as deflectedoptical radiation 375 at a target deflection angle, according to oneembodiment. In the illustrated embodiment, the substrate 351 is areflective substrate and/or the substrate 351 includes a reflectivelayer. The metasurface may operate to focus the optical radiation andmay be referred to as a metalens.

FIG. 3C illustrates the example block diagram of the metasurface 300 ofFIG. 3A steering incident optical radiation 371 as deflected opticalradiation 376 at a target deflection angle, according to one embodiment.In the illustrated embodiment, the optical radiation passes throughsubstrate 352. In some instances, the transmission-mode substrate 352may include one or more index-matching layers to improve transmittanceefficiency.

FIGS. 4A-4B illustrate metasurfaces used in conjunction withlaser-scanning subsystems, according to various embodiments. Asillustrated and labeled, a laser source 450 may transmit coherentoptical radiation to a scanning mirror 440 that is mechanically movedbetween a first position and a second position to scan the laser alongone dimension (left to right on the page). In some embodiments, twomirrors are used (one fast and one slow) on orthogonal axes to raster animage. In FIG. 4A, optical radiation 410 from the laser source 450 isincident on the left side of a metasurface 400 at a first angle ofincidence when the scanning mirror 440 is rotated counterclockwise(shown in solid lines). Optical radiation 410 from the laser source 450is incident on the right side of the metasurface 400 at a second angleof incidence when the scanning mirror 440 is rotated clockwise (shown indashed lines).

As illustrated, the metasurface 400 may be configured to deflect theincident optical radiation as collimated optical radiation 420 thattransmits in a uniform direction along the length of the metasurface400. In such an embodiment, an array of deflector elements may bepatterned on a substrate with dimensions, spacings, and heights tocompensate for the different angle of incidence of the optical radiation410 as the scanning mirror 440 is rotated.

In an alternative embodiment illustrated in FIG. 4B, the metasurface 400may comprise an array of deflector elements patterned on a substratewith dimensions, spacings, and heights to transmit output opticalradiation 410 at different exit angles 420 and 421 depending on thelocation at which the optical radiation 410 was received. The effectivedeflection pattern of the metasurface 400 may be selected to achieve atarget optical objective, such as forming multiple depth planes, pupilreplication, or expansion of a viewing eyebox.

FIG. 5A illustrates an example system with a metasurface 500 andwaveguide 560 used in conjunction with a laser scanning subsystem thatincludes a laser source 550 and a scanning mirror 540, according to oneembodiment. According to the illustrated embodiment, the metasurface 500may provide the equivalent functionality of injection optics in alaser-scanning illumination engine. In some embodiments, the metasurface500 (or just the array of deflector elements) may be directly fabricatedon or in a waveguide substrate. Given the subwavelength thickness of themetasurface 500, the system may be much more compact and/or efficientthan a similar system using traditional injection optics.

The metasurface 500 deflects received optical radiation 510 into thewaveguide 560 for total internal reflection and/or transmission, at 520,as guided optical radiation along the length of the waveguide 560. Inthe illustrated embodiment, the optical radiation 510 generated by thelaser source 550 passes through the metasurface 500 before entering thewaveguide 560.

FIG. 5B illustrates an example display system that utilizes an inputmetasurface coupler 565 and an output metasurface coupler 566 inconjunction with a waveguide 560, according to one embodiment. A displayengine 570 generates optical radiation as part of an RGB display (e.g.,via an LED array of RGB pixels). The input metasurface coupler 565couples the generated RGB optical radiation for transmission along thelength of the waveguide 560. The output metasurface coupler 566 receivesthe transmitted optical radiation and decouples the optical radiationfrom the waveguide 560 for visualization by a user (e.g., viafrequency-selective focusing to a target plane), at 575. In theillustrated embodiment, the optical radiation generated by the displayengine 570 passes through the input metasurface coupler 565 beforeentering the waveguide 560.

FIG. 6A illustrates a cross-sectional view of a portion of a cell 601 ofa metasurface for red optical radiation (e.g., having a wavelength of628 nanometers), according to one embodiment. The cross-sectional viewincludes three angled ridges 610 fabricated with gaps between adjacentangled ridges. In the illustrated example, the spacing between adjacentelements is 33 nanometers. The angled ridges 610 representcross-sections of elongated angled ridges that form a slanted gratingmetasurface for the red optical radiation, as described and illustratedin conjunction with FIGS. 7A and 7B below. In various embodiments, theangled ridges 610 may be fabricated using polysilicon, amorphoussilicon, silicon nitride, titanium dioxide, lithium niobate,polysilicon, and/or combinations thereof.

In the illustrated example, each angled ridge 610 is a right trianglewith a height of 153 nanometers and a base width of 457 nanometers. Theinternal angle between the hypotenuse of each angled ridge 610 and thebase is approximately 19 degrees, at 631. Optical radiation is incident,at 691, on the cell 601 an angle of incidence substantiallyperpendicular to the base. While only three angled ridges 610 areillustrated, the cell 601 for red optical radiation includes, in someembodiments, six (6) ridges that operate to deflect the opticalradiation at a deflection angle of approximately 44 degrees, at 692.

Each angled ridge 610 is sub-wavelength in dimension with a base widthsmaller than the operational wavelength. The gap between adjacent angledridges 610 is approximately 33 nanometers, such that red cell 602 has atotal width dimension of approximately 3.2 micrometers. Differentdimensions and gap spacing may be used for different wavelengths ofoptical radiation. For example, for red optical radiation having awavelength between approximately 600 and 700 nanometers, angled ridgesmay be utilized that have heights between 125 and 175 nanometers, basewidths between 400 and 500 nanometers, and inter-ridge gaps between 0and 50 nanometers. The angle 631 of the hypotenuse face of each angledridge relative to the base face may be adjusted between approximately 15degrees and 25 degrees based on the wavelength of optical reflection tobe deflected and the target angle of deflection.

Additionally, depending on the specific dimensions of the angled ridges,the gaps between them, and the material utilized, the angle ofdeflection, at 641, may vary between approximately 35 degrees and 55degrees. A target angle of deflection may be selected to ensure that thetransmitted optical radiation enters an optical waveguide and istransmitted therein at an angle less than a critical angle, resulting intotal internal reflection (TIR) within the waveguide.

FIG. 6B illustrates a cross-sectional view of a portion of a cell 602 ofa metasurface for green optical radiation (e.g., having a wavelength of525 nanometers), according to one embodiment. Again, the illustratedangled ridges 620 represent cross-sections of the three-dimensionalelongated angled ridges that form the slanted grating of a metasurfacefor green optical radiation. Each angled ridge 620 is a right trianglewith a height of 132 nanometers and a base width of 383 nanometers,which is less than an operational wavelength of green optical radiationat 525 nanometers. The hypotenuse of each angled ridge 620 is at anangle of approximately 19 degrees relative to the base. Incident opticalradiation, at 693, is deflected at a deflection angle, at 642, ofapproximately 46 degrees.

The cell 602 of the metasurface for green optical radiation may includeseven ridges for green light having a wavelength of approximately 525nanometers. A gap between adjacent angled ridges is illustrated asapproximately 24 nanometers, such that green cell 602 has a total widthdimension of approximately 3.2 micrometers. Different dimensions and gapspacing may be used for different wavelengths of optical radiation. Forexample, for green optical radiation having a wavelength betweenapproximately 495 and 570 nanometers, angled ridges may be utilized thathave heights between 110 and 150 nanometers, base widths between 350 and450 nanometers, and inter-ridge gaps between 0 and 40 nanometers.

The angle of the hypotenuse face of each angled ridge relative to thebase face may be adjusted between approximately 15 degrees and 25degrees to achieve the target deflection angle, at 642, of incidentoptical radiation, at 693. Additionally, depending on the specificdimensions of the angled ridges, the gaps between adjacent angledridges, and the material utilized, the angle of deflection may varybetween approximately 35 degrees and 55 degrees.

FIG. 6C illustrates a cross-sectional view of a portion of a cell 603 ofa metasurface for blue optical radiation (e.g., having a wavelength of455 nanometers), according to one embodiment. Again, the illustratedangled ridges 630 represent cross-sections of three-dimensional angledridges that form the slanted grating of a metasurface for blue opticalradiation. Each angled ridge 630 is a right triangle with a height of115 nanometers and a base width of 332 nanometers, which is less thanthe operational wavelength of blue optical radiation at 455 nanometers.The hypotenuse of each angled ridge 620 is at an angle of approximately19 degrees relative to the base. Incident optical radiation, at 695, isdeflected at a deflection angle, at 643, of approximately 48 degrees.

The cell 603 of the metasurface for blue optical radiation may includenine angled ridges for blue light having a wavelength of approximately455 nanometers. A gap between adjacent ridges is illustrated asapproximately 18 nanometers, such that blue cell 603 has a total widthdimension of approximately 3.2 micrometers. Different dimensions and gapspacing may be used for different wavelengths of optical radiation. Forexample, for blue optical radiation having a wavelength betweenapproximately 450 and 495 nanometers, angled ridges may be utilized thathave heights between 90 and 140 nanometers, base widths between 300 and400 nanometers, and inter-ridge gaps between 0 and 35 nanometers.

The angle of the hypotenuse face of each angled ridge relative to thebase face may be adjusted between approximately 15 degrees and 25degrees to achieve a target deflection angle, at 643, of incidentoptical radiation, at 695. Additionally, depending on the specificdimensions of the angled ridges, the gaps between adjacent angledridges, and the material utilized, the angle of deflection may varybetween approximately 30 degrees and 60 degrees.

FIG. 7A illustrates a top-down view of an example of a two-dimensionalRGB cell 700 of a metasurface, according to one embodiment. The top-downview of the RGB cell 700 includes six red, angled ridges 710, sevengreen, angled ridges 720, and nine blue, angled ridges 730 that form anRGB cell of a slanted grating metasurface. In the illustrated example,the gap between adjacent red, angled ridges 710 is approximately 33nanometers. The gap between the adjacent red 710 and green 720 angledridges is approximately 260 nanometers. The gap between adjacent green,angled ridges 720 is approximately 24 nanometers. The gap between thegreen 720 and blue 730 angled ridges is approximately 351 nanometers.The gap between adjacent blue, angled ridges 730 is approximately 18nanometers.

The illustrated RGB cell 700 may be replicated in one or two dimensionsto form a one-dimensional array of RGB cells 700 or a two-dimensionalarray of RGB cells 700. In such embodiments, the gap between the blue,angled ridges 730 and the red triangular ridges may be 50 nanometers.The gap between cells in the other dimension (e.g., the gap between endsof triangular ridges having the same color) may be minimized or spacedaccording to the underlying light source (e.g., an array of underlyingLEDs or OLEDs).

The exact number (and relative numbers) of red, green, and blue angledridges 710-730 may be modified and vary based on the absolute size andrelative sizes of the red, green, and blue subpixels of an underlyingdisplay (e.g., based on the pitch and interpixel spacing of the pixelsof the display and/or the pitch and inter-subpixel spacing of thesubpixels of the display).

FIG. 7B illustrates a perspective view of a two-dimensional RGB cell 700of a metasurface, according to one embodiment. In the illustratedembodiment, the first six angled ridges 710 correspond to a red portionof the RGB cell 700. The next seven angled ridges 720 correspond to agreen portion of the RGB cell 700. The last nine angled ridges 730correspond to a blue portion of the RGB cell 700.

FIG. 8 illustrates an example of a metasurface 800 comprising amultipixel array of four “RGB supercells” 801, 802, 803, and 804, whereeach of the four RGB supercells 801-804 includes an array of RGB cells810 (a red cell), 820 (a green cell), and 830 (a blue cell). In theillustrated embodiment, a gap between elements associated with differentcolor subpixels (e.g., the gap between adjacent red and green subpixels)may be nonexistent (gapless), minimized, and/or made to correspond tothe spacing of the subpixels in an underlying LED or OLED display.

In the illustrated embodiment, the metasurface 800 includes a two-by-twoarray of four RGB supercells 801-804, each of which is approximately 9.6micrometers by 9.6 micrometers, such that the metasurface 800 has atotal area of 38.4 square micrometers. Any number of RGB supercells801-804 may be utilized in square or rectangular arrays to match thedimensions of an underlying LED or OLED display.

The metasurface 800 may be overlaid on and aligned with a correspondingarray of LEDs or OLEDs having red, green, and blue subpixels withdimensions and spacings corresponding to the dimensions and spacing ofthe RGB cells 810-830. In such an embodiment, each individual RGB cell810-830 operates to deflect optical radiation of a correspondingwavelength (color) from an underlying respective subpixel of the LED orOLED display.

While the presently described systems and methods are generallydescribed in the context of rectangular pixels that each comprise threerectangular subpixels—a red subpixel, a green subpixel, and a bluesubpixel—it is appreciated that alternative pixel and/or subpixel shapesare possible, such as squares, hexagons, circles, triangles, ovals, andthe like. In such embodiments, each cell of the metasurface may includea selectable number of triangular ridges with varying lengths and/orspacings to allow the dimensions and shape of each cell to approximatethe dimensions and shapes of the corresponding subpixels of the LED orOLED display. Similarly, while the presently described systems andmethods are generally described in the context of RGB imaging systemsand utilize red, green, and blue subpixels for color mixing, it isappreciated that displays may utilize different colors (wavelengths),additional subpixels, and/or different subpixel matrix schemes. Forexample, an active-matrix OLED or AMOLED display may utilize an RG-BGcolor scheme that includes a lower percentage of red and blue subpixelsrelative to the green subpixels. The presently described metasurfacesmay be adapted to include a corresponding arrangement of red-green andblue-green cells of triangular ridges.

As another example, an RGBY electronic display may include yellowsubpixels in addition to the traditional red, green, and blue subpixels.Again, the presently described metasurface may be adapted such that eachsupercell includes a red cell, a green cell, a blue cell, and a yellowcell of angled ridges. The dimensions of the angled ridges andinterelement spacings may be selected to deflect the yellow opticalradiation emitted by the yellow subpixels. For example, for yellowoptical radiation having a wavelength between approximately 550 and 590nanometers, angled ridges may be utilized that have heights between 115and 160 nanometers, base widths between 375 and 475 nanometers, andinter-ridge gaps between 0 and 35 nanometers to achieve a targetdeflection angle (e.g., 45 degrees).

FIG. 9A illustrates a metasurface 965 comprising a multi-pixel array ofRGB cells (e.g., as illustrated and described in conjunction with FIGS.6A-8 ) used to couple optical radiation 910 into a waveguide 960,according to one embodiment. As illustrated, the optical radiation 910includes three different wavelengths (illustrated as different dashedpatterns) that are incident on the metasurface 965 substantiallyperpendicular to the length of the waveguide 960 and normal to theincidence surface of the waveguide. The metasurface 965 may comprise aslanted grating of angled ridges to deflect the incident opticalradiation 910 at an angle into the waveguide 960 for total internalreflection (TIR) and conveyance along a length thereof.

FIG. 9B illustrates a side view of an optical system that includes adisplay 970, a metasurface 966, and a waveguide 961 (e.g., glass orsapphire), according to one embodiment. The display 970 may, forexample, comprise a multipixel RGB display configured to generate red,green, and blue optical radiation at an angle perpendicular to thelength of the waveguide 961 (e.g., normal or orthogonal to the upper 963and lower surfaces 962 of the waveguide 961). A metasurface 966positioned between the display 970 and the waveguide 961 deflects theoptical radiation generated by the display 970 into the waveguide 961 atan angle less than a critical angle for total internal reflection.

The metasurface 966 may comprise, as described herein, a slanted gratingof elongated angled ridges extending along the width of the waveguide961 with interelement spacings defined along the length of the waveguide961. The metasurface 966 couples the optical radiation from the display970 into the waveguide 961 for transmission along the length thereof. Insome embodiments, the display 970 may be in direct contact with theupper edges of the elongated angled ridges of the metasurface 966 or indirect contact with a planar, optically transparent covering on theelongated angled ridges of the metasurface 966. In other embodiments,the display 970 may generate optical radiation that travels through freespace (e.g., through a vacuum, air, a gas, or a liquid) for at least ashort distance before being received and deflected by the metasurface966.

FIG. 9C illustrates a top view of the optical system of FIG. 9B,according to one embodiment. As illustrated, optical radiation ofvarying wavelengths (illustrated as different dashed lines to representred, green, and blue optical radiation) is transmitted along the lengthof the waveguide 961. The metasurface 966 and the underlying display 970are visible in broken lines through the upper surface 963 of thewaveguide 961. The elongated angled ridges of the slanted gratingmetasurface extend along the width of the metasurface and are spacedalong the length thereof. In the illustrated example, the elongatedangled ridges of the slanted grating metasurface extend along the widthof the metasurface but do not extend to the edges thereof. In otherembodiments, the elongated angled ridges of the slanted gratingmetasurface may extend across the width of the waveguide from edge toedge.

FIG. 10A illustrates a cross-section view of an alternative embodimentof a portion of a metasurface 1065 with rectangular ridges 1067 (e.g.,that extend into and out of the page) to deflect incident opticalradiation 1010 as deflected optical radiation 1020 into a waveguide,according to one embodiment. The metasurface 1065 includes a pluralityof rectangular ridges 1067 having varying widths and inter-elementspacings that extend from a substrate 1050. In the illustratedembodiment, a pattern of three rectangular ridges 1067 having widths of70 nanometers, 20 nanometers, and 23 nanometers is repeated every 410nanometers (the pitch of the repeating pattern).

Spacings between the rectangular ridges 1067 in the repeating patternare illustrated as example values of 179 nanometers, 68 nanometers, and50 nanometers, respectively. In some embodiments, the rectangular ridges1067 are formed from polysilicon. The specific heights, widths, andinterelement spacings of the rectangular ridges 1067 and the number ofrectangular ridges 1067 may be adjusted to efficiently couple one ormore specific wavelengths of optical radiation into a waveguide.

FIG. 10B illustrates an optical system 1000 comprising the metasurface1065 of FIG. 10A with rectangular ridges coupling optical radiation froma display engine 1070 into a waveguide 1060, according to oneembodiment. The optical system 1000 includes an output metasurfacecoupler 1077 as well. The display engine 1070 generates opticalradiation as, for example, part of an RGB display of LEDs. Themetasurface 1065 deflects the RGB optical radiation generated by thedisplay engine 1070 into the waveguide 1060 at an angle less than acritical angle for total internal reflection within the waveguide 1060,at 1020. The optical radiation is conveyed, at 1020, to the other end ofthe waveguide 1060 where it is decoupled from the waveguide 1060 by theoutput metasurface coupler 1077 or another device (e.g., a surfacerelief grating) for free-space transmission, projection, or display, at1075 (e.g., for visualization by a user through via frequency-selectivefocusing to a target plane).

FIG. 11A illustrates a graph of the diffraction efficiency of ametasurface of rectangular ridges with respect to the angle of incidenceof blue optical radiation (e.g., with a wavelength of approximately 490nanometers). As illustrated, the diffraction efficiency of themetasurface of rectangular ridges is relatively low (approximately 30%)for this blue optical radiation.

FIG. 11B illustrates a graph of the diffraction efficiency of ametasurface of rectangular ridges with respect to the angle of incidenceof red optical radiation (e.g., with a wavelength of approximately 650nanometers). Again, the diffraction efficiency of the metasurface ofrectangular ridges is relatively low (approximately 30%) for red opticalradiation.

FIG. 11C illustrates a graph of the diffraction efficiency of ametasurface of rectangular ridges with respect to the angle of incidenceof green optical radiation (e.g., with a wavelength of approximately 535nanometers). Again, the diffraction efficiency of the metasurface ofrectangular ridges is relatively low (approximately 30%) for greenoptical radiation.

FIG. 12 illustrates an optical system 1200 that utilizes a metasurfacecoupler 1265 to couple incident optical radiation 1201 into a waveguide1260, according to one embodiment. The metasurface coupler 1265 operatesto reflectively couple incident optical radiation 1201 into thewaveguide 1260 after the incident optical radiation 1201 passes throughthe waveguide 1260. As with the other figures described herein, FIG. 12is not drawn to scale.

The metasurface coupler 1265 comprises a plurality of elongated angledridges 1285 formed on top of a substrate 1280 on the waveguide 1260. Thecross-sectional view of FIG. 12 shows the elongated angled ridges 1285as triangles with the understanding that the shape extends in and out ofthe page, such that each of the elongated angled ridges 1285approximates the shape of an elongated right triangular polyhedron. Anoptically reflective layer 1287 is deposited on the triangular ridges1285 to reflect incident optical radiation with high efficiency. Theoptically reflective layer 1287 is illustrated as a conformallydeposited layer of silver; however, any of a wide variety of reflectivemetals or metal alloys may be utilized and/or the layer may or may notbe conformal. Examples of suitable reflective materials include silver,gold, aluminum, other noble metals, and/or combinations thereof.

According to various embodiments, the waveguide 1260 may comprise glass,sapphire, fused silica, or the like. The substrate 1280 of themetasurface coupler 1265 may comprise a material having a relativelyhigh refractive index. In some embodiments, the substrate 1280 isdeposited on the waveguide 1260 during the fabrication of themetasurface coupler 1265 (e.g., as the first layer). In otherembodiments, the metasurface coupler 1265 may be fabricated on thesubstrate 1280, and, once fabrication is complete, the substrate may befused or otherwise bonded to the waveguide 1260.

The incident optical radiation 1201 is incident on a lower surface ofthe waveguide 1260 and passes through the waveguide 1260 and thesubstrate 1280 and the polysilicon, elongated angled ridges 1285, whichare coated with a reflective silver layer 1287. The reflective silverlayer 1287 reflects the optical radiation back through the polysilicon,elongated angled ridges 1285 and the substrate 1280 into the waveguide1260, at 1202, at an angle less than a critical angle for total internalreflection therein and conveyance along the length thereof.

The elongated angled ridges 1285 for a slanted grating may extend formicrons, millimeters, or centimeters along the width of the waveguide1260 (e.g., in and out of the page). In the illustrated embodiment, thebase face (labeled B) of each elongated angled ridge may have a width ofapproximately 400 nanometers. As there are no gaps between adjacentelongated angled ridges in the illustrated embodiment, the pitch(labeled P) of the elongated angled ridges 1285 in the metasurfacecoupler 1265 is also 400 nanometers.

Each elongated angled ridge 1285 has a height face (labeled H) thatextends from the base face (B) to a height of approximately 145nanometers. As the height face (H) and the base face (B) areperpendicular to one another, the elongated angled ridges 1285approximate the shape of a right-angle triangular polyhedron in whichthe hypotenuse or angled face (A) extends from one edge of the base face(B) to an edge of the height face (H) with an internal angle (θ) ofapproximately 19.2 degrees.

The specific dimensions of the elongated angled ridges 1285 may bemodified or adjusted to increase the efficiency and/or operability ofthe metasurface coupler 1265 to deflect specific wavelengths of opticalradiation into the glass waveguide 1260 for total internal reflection.In some embodiments, the elongated angled ridges 1285 may be formed on athin, planar layer of polysilicon deposited on the substrate 1280. Thethin planar layer of polysilicon may, for example, have a thickness offewer than 30 nanometers. In some embodiments, the elongated angledridges 1285 may be formed directly on the substrate 1280, such thatthere is no additional planar layer of polysilicon deposited between theelongated angled ridges 1285 and the substrate 1280.

According to various embodiments, the same metasurface coupler 1265 withelongated angled ridges 1285 having the same dimensions may be used forred, green, and blue optical radiation. In other embodiments, for redoptical radiation, the hypotenuse face of each elongated angled ridge1285 relative to the base face may be approximately 16 degrees. Forgreen optical radiation, the hypotenuse face of each elongated angledridge 1285 relative to the base face may be approximately 20 degrees.For blue optical radiation, the hypotenuse face of each elongated angledridge 1285 relative to the base face may be approximately 22.5 degrees.

FIGS. 13A-D illustrate an example diagram of a manufacturing process fora slanted grating metasurface coupler, according to one embodiment. FIG.13A illustrates a waveguide 1360 that may be any length, width, andthickness suitable for conveying optical radiation from one end toanother end. The waveguide 1360 may be, for example, a glass waveguideas illustrated, or manufactured using one or more alternative materials,such as sapphire, fused silica, high-index glass, or other suitablewaveguide material.

As illustrated in FIG. 13B, an optically transparent layer 1380, such asthe illustrated silicon nitride optically transparent layer, isdeposited on the waveguide 1360. The optically transparent layer 1380may comprise a single layer or multiple layers and may include one ormore of silicon nitride, amorphous silicon, lithium niobate (LiNBO3)and/or another optically transparent material.

In FIG. 13C, a polysilicon (Poly-Si) layer 1385 is deposited on thesilicon nitride optically transparent layer 1380. In FIG. 13D, thepolysilicon layer 1385 is etched (e.g., via reactive-ion etching, ionmilling via a focused ion beam, nanoimprinting, or the like) to form aone-dimensional array of parallel, elongated angled ridges (extendinginto and out of the page in the illustrated example). In the illustratedexample, the elongated angled ridges 1385 have uniform heights andwidths and are gapless, such that there is no spacing between adjacentelongated angled ridges 1385. In some embodiments, the elongated angledridges 1385 and/or the silicon nitride optically transparent layer 1380may be annealed to improve optical transmittance efficiencies and/ormodify other optical characteristics thereof.

In FIG. 13E, a reflective layer 1387 (e.g., silver, gold, aluminum,another noble metal, or another suitably reflective ground planematerial) is deposited on top of the elongated angled ridges 1385.Alternatively, in FIG. 13F, a reflective coating 1388 may be thinlyapplied to the elongated angled ridges 1385 sufficient to reflectoptical radiation back through the silicon nitride optically transparentlayer 1380 and into the waveguide 1360. For example, a 100-nanometerlayer of silver may be applied to the exposed surface of the elongatedangled ridges 1385 for total or near-total reflection.

FIG. 14 illustrates a perspective view of a portion of a slanted gratingmetasurface coupler 1465 that includes a one-dimensional array of angledridges 1485 having subwavelength dimensions, according to variousembodiments. As illustrated, the one-dimensional array of angle ridges1485 is formed on a substrate 1486 (such as silicon nitride), which isdeposited directly on a glass waveguide 1460. The angled ridges 1485 areillustrated with a relatively thin coating of a reflective metal layer1487, such as silver, gold, aluminum, or another noble metal.

FIG. 15 illustrates an optical system 1500 with a slanted gratingmetasurface coupler 1565 to couple optical radiation into a waveguide1560, according to one embodiment. As illustrated, a display engine 1570transmits optical radiation (e.g., red, green, and blue opticalradiation) through the waveguide 1560. The optical radiation travelsthrough the waveguide 1560 and a substrate 1586 of the slanted gratingmetasurface coupler 1565. The optical radiation is deflected by thesubwavelength elongated angled ridges 1585 coated with a reflectivemetallic layer 1587.

The optical radiation is reflected by the reflective metallic layer 1587(e.g., silver, gold, aluminum, or a combination thereof) on thesubwavelength angled ridges 1585 of the slanted grating metasurfacecoupler 1565. The optical radiation is deflected by the subwavelengthangled ridges 1585 of the slanted grating metasurface coupler 1565before it passes back through the substrate 1586 and into the waveguide1560 at an angle for total internal reflection and transmission, at1520, along the length of the waveguide 1560 to an output coupler 1566.The optical radiation may then be directed into another optical deviceand/or emitted as free-space optical radiation 1575.

FIG. 16A illustrates a simulated graph of the efficiency with which aslanted grating metasurface coupler of elongated angled ridges couples608-nanometer optical radiation into a waveguide for total internalreflection therein, according to one embodiment. As illustrated, thesimulated coupler efficiency for this wavelength of red light isapproximately 80% in all simulated conditions.

FIG. 16B illustrates a simulated graph of the efficiency with which agrating metasurface coupler of elongated angled ridges couples568-nanometer optical radiation into a waveguide for total internalreflection therein, according to one embodiment. As illustrated, thesimulated coupler efficiency for this wavelength of green light isapproximately 85% in all simulated conditions.

FIG. 16C illustrates a simulated graph of the efficiency with which aslanted grating metasurface coupler of elongated angled ridges couples498-nanometer optical radiation into a waveguide for total internalreflection therein, according to one embodiment. As illustrated, thesimulated coupler efficiency for this wavelength of blue light isapproximately 82% in all simulated conditions.

FIG. 17 illustrates an optical system 1700 in which a slanted gratingmetasurface coupler operates to couple incident optical radiation 1701into a high-index glass waveguide substrate 1760 for total internalreflection therein, at 1702. The metasurface coupler includes aone-dimensional array of elongated angled ridges 1780 of amorphoussilicon formed directly on the high-index glass waveguide substrate1760. An optically reflective metallic layer 1785 is deposited as alayer or coating on the right-elongated angled ridges 1780.

In various embodiments, amorphous silicon or another material orcombination of materials, such as silicon nitride, titanium dioxide,lithium niobate, polysilicon, or the like is deposited directly on thehigh-index glass waveguide substrate 1760. In one example, the layer ofamorphous silicon is initially formed with a thickness of approximately145 nanometers. The amorphous silicon is etched to form the elongatedangled ridges 1780, after which the metallic layer 1785 or similarcoating is deposited on the elongated angled ridges 1780 with athickness of approximately 100 nanometers.

According to various embodiments, an angled face (or a hypotenuse facein the case of right-angle triangle cross-sections, as illustrated) ofthe elongated angled ridges 1780 relative to a base face may beapproximately 16 degrees for red wavelengths of optical radiation,approximately 20 degrees for green wavelengths of optical radiation, andapproximately 22.5 degrees for blue wavelengths of optical radiation.

In some embodiments, a slanted grating metasurface coupler with an arrayof elongated angled ridges having uniform dimensions and angles betweenthe base, height, and hypotenuse faces (or angled faces in the case ofelongated angled ridges having non-right-angle triangularcross-sections) may be used for multiple wavelengths of opticalradiation. For instance, a common slanted grating metasurface coupler ofelongated angled ridges may be used to couple red, green, and blueoptical radiation into a waveguide for total internal reflectiontherein. Devices that utilize different angles of ridges for each colorare aligned with the corresponding color of an underlying subpixel.However, a common metasurface coupler that uses the same elongatedangled ridges for each color does not require subpixel alignment.

FIG. 18 illustrates an example of an optical system 1800 with ametasurface coupler with a slanted grating formed as an array ofelongated angled ridges 1880, whose cross-section is a triangle. Theelongated angled ridges 1880 of silicon nitride are formed directly on aglass or sapphire waveguide substrate 1860, according to variousembodiments. The illustrated embodiment includes a waveguide substratewith a thickness of approximately 0.5 millimeters. The elongated angledridges 1880 extend along a width of the waveguide substrate 1860 (i.e.,in and out of the page).

Each elongated angled ridge 1880 includes a base face that is co-planarwith the surface of the waveguide 1860, a height face that extends fromthe base face to a ridge height with an internal angle greater than 60degrees relative to the base face (illustrated as a perpendicular 90degrees), and an angled face that extends between an edge of the baseface and the edge of the height face at a target internal angle lessthan 25 degrees relative to the base face. In the illustratedembodiment, the base face has a width of 345 nanometers and the heightface extends to a ridge height of 150 nanometers. The internal anglebetween the angled face and the base face is approximately 23.45degrees. As there is no gap or spacing between adjacent elongated angledridges 1880 in the illustrated embodiment, the pitch of the array ofelongated angled ridges 1880 forming the slanted grating is equal to thewidth of the base face of an individual elongated angled ridges 1880,which is 345 nanometers in the illustrated embodiment.

The slanted grating of the metasurface coupler includes a reflectivemetallic ground plane 1885 (e.g., a layer or coating), which is adheredto the array of elongated angled ridges 1880 via a thin metallicadhesion layer 1882. According to various embodiments, the metallicadhesion layer 1882 may be a layer of titanium (Ti) or Chromium (Cr)that is 1-5 nanometers thick (illustrated as 2-3 nanometers). Thereflective metallic ground plane 1885 may have a thickness ofapproximately 100 nanometers or more and comprise one or more of gold,silver, aluminum, another noble metal, and/or alloys or multilayersthereof.

FIGS. 19A-J illustrate a diagram of a manufacturing process for ametasurface coupler, according to one embodiment.

FIG. 19A illustrates a silicon nitride layer 1980 deposited on a planarface of a waveguide substrate 1960. A thin conductive layer 1981 isdeposited on the silicon nitride layer 1980 to facilitate electron beamlithography of a subsequently deposited photoresist.

FIG. 19B illustrates a photoresist 1983 applied as a coating on the thinconductive layer 1981. The photoresist 1983 is processed to define aplurality of elongated rectangular cuboids of photoresist that extendorthogonally with respect to the planar face of the waveguide substrate1960 (i.e., in an out of the page). For example, electron beamlithography may be used to define the plurality of elongated rectangularcuboids of photoresist to each have a width between 70 and 130nanometers and an interelement spacing between 300 and 400 nanometers.

FIG. 19C illustrates elongated rectangular cuboids of photoresist 1984extending orthogonally with respect to the planar face of the waveguidesubstrate 1960, according to one embodiment.

FIG. 19D illustrates the very thin conductive layer 1981 (e.g., Pd/Au)etched or otherwise removed from channels between the elongatedrectangular cuboids of photoresist 1984, according to one embodiment.With the conductive layer 1981 removed from the channels between theelongated rectangular cuboids of photoresist 1984, the silicon nitride1980 can be etched within the channels to a target depth.

FIG. 19E illustrates the partial etching (e.g., using reactive-ionetching (RIE)) of the silicon nitride layer 1980 between the rectangularcuboids of photoresist 1984 to a target depth. As illustrated, a thinlayer of silicon nitride 1980 remains in the channels between therectangular cuboids of photoresist 1984. With the partial etching of thesilicon nitride layer 1980 completed, the rectangular cuboids ofphotoresist 1984 can be removed from the silicon nitride layer 1980.

FIG. 19F illustrates an exposed plurality of elongated rectangularridges of silicon nitride 1991 extending from a base layer of siliconnitride 1992 having an initial thickness. The elongated rectangularridges of silicon nitride 1991 extend into and out of the page (e.g.,along the width of the planar waveguide).

FIG. 19G illustrates ion beam milling of the silicon nitride layer 1980via an ion beam milling system 1911. The silicon nitride layer 1980 ismilled via the ion beam 1912 at an angle with respect to the normal(dashed line) of the planar face of the waveguide substrate 1960. Theion beam milling process operates to shape the silicon nitride layer1980 into elongated angled ridges by an additive process that “pushes”the silicon nitride from the field onto the wall of the rectangularridge that was previously formed through the vertical etching process(e.g., the reactive-ion etching process above). The thickness of theremaining base layer of silicon nitride after milling, if any, isselected based on the milling rate of the silicon nitride and the beamangle utilized.

FIG. 19H illustrates the triangular cross-section of the ion beam-etchedelongated angled ridges 1993 of silicon nitride on the surface of thewaveguide substrate 1960. As described herein, the elongated angledridges 1993 are formed through a two-stage etching process. The firststage includes vertical etching (e.g., reactive-ion etching) to form therectangular ridges (FIG. 19F) that serve as backstops during the secondstage. The second stage is the ion beam etching or milling to push thesilicon nitride from the base layer onto the wall of the rectangularridges to form slanted grating of elongated angled ridges 1993, asillustrated in FIG. 19H.

FIG. 19I illustrates a thin adhesion layer 1982, such as titanium orchromium, applied to the elongated angled ridges 1993 of siliconnitride. The thin adhesion layer 1982 is, in some embodiments, a firstsublayer of a metallic layer to be deposited over the elongated angledridges 1993 of silicon nitride.

FIG. 19J illustrates an optically reflective metallic layer 1985deposited over the thin adhesion layer 1982. The optically reflectivemetallic layer 1985 is, in some embodiments, a second sublayer of themetallic layer deposited over the elongated angled ridges 1993 ofsilicon nitride.

FIGS. 20A-C illustrate a diagram of an additive ion beam etching processto form elongated angled ridges of silicon nitride on a waveguide,according to various embodiments.

FIG. 20A illustrates an ion beam 2012 etching a silicon nitride layer2080 to form a slanted grating of elongated angled ridges of siliconnitride on the waveguide substrate 2060. As described herein, the ionbeam 2012 operating at an angle relative to nanometer-scale ridges andchannels of silicon nitride 2080 functions as an additive process.

FIG. 20B illustrates the additive process accomplished by the ion beametching process that operates to create the slanted grating of elongatedangled ridges of silicon nitride on the waveguide substrate 2060. Asillustrated, the ion beam 2012 operates to remove silicon nitride fromthe region 2078 in each channel and deposit at least some of the siliconnitride in the region 2079. The movement of silicon nitride from theregion 2078 to the region 2079 via the additive ion beam etchingprocess, and similar movements of silicon nitride from correspondingregions relative to each respective rectangular ridge of siliconnitride, results in the formation of a one-dimensional array ofelongated angled ridges of silicon nitride.

FIG. 20C illustrates elongated angled ridges 2099 of silicon nitrideextending from a thinned base layer 2092 of silicon nitride on thewaveguide substrate 2060. As described herein, the base layer 2092 ofsilicon nitride may be less than 30 nanometers thick, while theelongated angled ridges 2099 may extend to a height between 70 and 200nanometers. In some embodiments, the base layer 2092 may be omitted(i.e., have a thickness of 0 nanometers). The specific dimensions of theelongated angled ridges 2099, as described according to any of thevarious embodiments described herein, may be formed using thefabrication processes and techniques described in conjunction with FIGS.19A-20C.

FIG. 21 illustrates an example image 2100 of elongated angled ridges2180 of silicon nitride on a glass substrate 2160, according to oneembodiment. The elongated angled ridges 2180 in the image 2100 wereformed using the fabrication processes and techniques described herein.

FIG. 22 illustrates an example graph of the height (vertical axis) of across-section of a plurality of elongated angled ridges 2280 of siliconnitride forming a slanted grating along the length (horizontal axis) ofa glass substrate, according to one embodiment. Notably, the illustratedvertical and horizontal axes use different scales, but the numericalmeasures are still valid. As described herein, the cross-section of eachelongated angled ridge 2280 forms a shape approximating a righttriangle. As previously clarified, some fabrication and manufacturingapproaches have inherent limitations that may result in features andelements characterized by rounded corners, minor irregularities, and/orvertical or perpendicular faces that are slightly less than vertical orat a slight angle relative to perfect 90 degrees. However, with furtherrefinement of such processes and/or the utilization of additional oralternative processes, near-perfect fabrication shaping is achievable.

In the illustrated embodiment, the distance along the horizontal axisbetween the point 2201 and the point 2203 corresponds to the width of abase face of what is loosely referred to as a right trianglecross-section of an elongated angled ridge of a slanted gratingmetasurface coupler. The distance between the point 2203 and the point2202 along the vertical axis corresponds to the height that the heightface of the elongated angled ridge extends from the base face. An anglebetween the line connecting point 2201 and the point 2202 and the lineconnecting points 2201 and 2203 corresponds to an inner angle of ahypotenuse or angled face of the elongated angled ridge relative to thebase face thereof.

FIG. 23 illustrates a perspective view of an optical device 2300 with aslanted grating metasurface coupler, according to one embodiment. Theslanted grating metasurface coupler includes a slanted grating formed asan array of angled ridges 2380 of silicon nitride directly on a glasswaveguide 2360, according to one embodiment. An adhesion layer (notshown) adheres the elongated angled ridges 2380 of silicon nitride to anoptically reflective metallic layer 2385. The optically reflectivemetallic layer 2385 may be, for example, at least 100 nanometers thick.The slanted grating of elongated angled ridges 2380 is simplified toonly include seven ridges; however, it is appreciated that the slantedgrating of the metasurface coupler may have square or rectangulardimensions on the order of centimeters and therefore include many moreelongated angled ridges 2380 that have corresponding lengths across thewidth dimension of the underlying glass waveguide 2360.

FIG. 24A illustrates a diagram of an optical system with a metasurfacecoupler 2465 of silicon nitride ridges with cross-sections approximatingtriangles to couple optical radiation from a display engine 2470 into awaveguide 2460, according to various embodiments. The optical radiationfrom the display engine 2470 is deflected by the metasurface coupler2465 at an angle less than a critical angle for total internalreflection therein and conveyance, at 2420, to an output coupler 2466 onan opposite end of the waveguide 2460.

FIG. 24B illustrates a close-up image of a portion of the metasurfacecoupler 2465, according to one embodiment. As illustrated, while theelongated angled ridges of the metasurface couplers are modeled ashaving cross-sections approximating right triangles (as illustrated in,for example, FIG. 19J, FIG. 20C, or FIG. 23 ), actual cross-sectionalimages of the elongated angled ridges 2480 of the metasurface coupler2465 demonstrate the realities of approximation due to fabrication andmanufacturing limitations. Again, refined manufacturing and fabricationtechniques allow for a closer approximation to the modeled shapes.

This disclosure has been made with reference to various embodiments,including the best mode. However, those skilled in the art willrecognize that changes and modifications may be made to the variousembodiments without departing from the scope of the present disclosure.While the principles of this disclosure have been shown in variousembodiments, many modifications of structure, arrangements, proportions,elements, materials, and components may be adapted for a specificenvironment and/or operating requirements without departing from theprinciples and scope of this disclosure. These and other changes ormodifications are intended to be included within the scope of thepresent disclosure as encompassed by the claims below, which form a partof this disclosure.

What is claimed is:
 1. An optical system, comprising: a waveguide; anoptical source to generate optical radiation incident on a first face ofthe waveguide at an angle of incidence at which the optical radiationpasses through the waveguide and out of a second face of the waveguidethat is opposite the first face of the waveguide; and a metasurface onthe second face of the waveguide to receive the optical radiation thatpasses through the waveguide from the optical source, wherein themetasurface is operable to reflect the optical radiation back into thewaveguide at an angle greater than a critical angle for total internalreflection within the waveguide, such that the optical radiation isconveyed along a length of the waveguide.
 2. The system of claim 1,wherein the waveguide comprises at least one of glass and sapphire. 3.The system of claim 1, wherein the optical source comprises at least oneof an array of lasers, an array of light-emitting diodes (LEDs), anarray of micro light-emitting diodes, and an array of organiclight-emitting diodes (OLEDs).
 4. The system of claim 1, wherein themetasurface comprises: a slanted grating of angled ridges extendingparallel to one another along a width of the waveguide and perpendicularto the length of the waveguide; and a reflective metallic layer over thearray of angled ridges.
 5. The system of claim 4, wherein the angledridges of the slanted grating comprise angled ridges of silicon nitridepositioned directly on the second face of the waveguide.
 6. The systemof claim 4, wherein the angled ridges of the slanted grating are formedas a one-dimensional array of angled ridges of silicon nitride on a baselayer of silicon nitride, wherein the base layer of silicon nitride isless than 30 nanometers thick and is positioned directly on the secondface of the waveguide.
 7. The system of claim 4, wherein each angledridge of the slanted grating comprises: a base face that is co-planarwith the second face of the waveguide; a height face that extends fromthe base face to a ridge height with an internal angle greater than 60degrees relative to the base face; and an angled face that extendsbetween an edge of the base face and an edge of the height face at atarget internal angle less than 25 degrees relative to the base face. 8.The system of claim 7, wherein the height face of each angled ridge ofthe slanted grating is at a right angle with respect to the base face ofeach respective angled ridge of the slanted grating.
 9. The system ofclaim 8, wherein the height face of each angled ridge of the slantedgrating extends from the base face of each respective angled ridge ofthe slanted grating to a ridge height between 70 and 200 nanometers. 10.The system of claim 9, wherein the target internal angle of the angledface of each angled ridge of the slanted grating relative to the baseface of each respective angled ridge of the slanted grating is between15 and 25 degrees.
 11. The system of claim 10, wherein a length of thebase face along the length of the waveguide of each angled ridge of theslanted grating is equal to a pitch between adjacent angled ridges inthe slanted grating, such that there is substantially no gap betweenadjacent angled ridges, and wherein the pitch between adjacent angledridges is between 300 and 500 nanometers.
 12. An optical system,comprising: a slanted grating metasurface formed on a planar face of awaveguide to couple optical radiation passing through the waveguide backinto the waveguide for conveyance along a length of the waveguide, theslanted grating metasurface comprising: an array of elongated siliconnitride ridges extending along a width of the waveguide, wherein across-section of each elongated silicon nitride ridge approximates atriangle; and a reflective metallic layer positioned on the elongatedsilicon nitride ridges, wherein an internal angle of an angled face ofeach elongated silicon nitride ridge is less than 25 degrees relative tothe planar face of the waveguide, wherein each elongated silicon nitrideridge extends to a height between 70 and 200 nanometers from the planarface of the waveguide, and wherein a pitch between adjacent elongatedsilicon nitride ridges is between 300 and 500 nanometers.
 13. The systemof claim 12, wherein the waveguide comprises at least one of glass andsapphire.
 14. The system of claim 12, wherein the array of elongatedsilicon nitride ridges is formed on a base layer of silicon nitride,wherein the base layer of silicon nitride is less than 30 nanometersthick and is positioned directly on the planar face of the waveguide.15. The system of claim 12, wherein a height face of each elongatedsilicon nitride ridge of the slanted grating is at a right angle withrespect to a base face of each respective elongated silicon nitrideridge of the slanted grating.
 16. The system of claim 12, wherein theinternal angle of the angled face of each elongated silicon nitrideridge of the slanted grating relative to a base face of each respectiveelongated silicon nitride ridge of the slanted grating is between 15 and25 degrees.
 17. The system of claim 16, wherein the base face of eachelongated silicon nitride ridge of the slanted grating is parallel tothe planar face of the waveguide.
 18. The system of claim 12, wherein alength of a base face along the length of the waveguide of eachelongated silicon nitride ridge of the slanted grating is equal to apitch between adjacent elongated silicon nitride ridge of the slantedgrating, such that there is substantially no gap between adjacentelongated silicon nitride ridges.